Documento PDF - UniCA Eprints - Università degli studi di Cagliari.

76 molecular dynamicsities by a factor λ. The associated temperature change iscalculated as:∆T = 1 2 ∑ 2 m i(λv i ) 2− 1 Nki=1 B 2 ∑ 2 m iv 2 iNki=1 B(A.12)∆T = (λ 2 − 1)T(t)(A.13)λ =√T 0 /T(t)(A.14)Unfortunally, with this method the fluctuations of the kineticenergy of the system are suppressed and the trajectoriesproduced are not consistent with the canonical ensemble.A better method to control the temperature is the Berendsenapproach [116] that consists in coupling the systemwith an external heat bath at fixed temperature T 0 . Thevelocities are scaled accordingly to the following equation:dT(t)dt= T 0 − T(t)τ(A.15)where τ is a time constant. The temperature change afterone timestep is∆T = δtτ (T 0 − T(t))(A.16)where δt is the integration step. Putting the Equation A.13in the Equation A.16 it is found:(λ 2 − 1)T(t) = δtτ ((T 0 − T(t))Finally, the scaling factor λ 2 is:√λ = 1 + δt ( T 0τ T(t) − 1)(A.17)(A.18)The correct choice of τ is very important. In fact, the limitτ = δt brings back the velocity rescaling method while forτ → ∞ the dynamics will sample the microcanonical ensembleand the Berendsen approach would be ineffective.